The Multi-level Dilated Nested Array for Direction of Arrival Estimation

In this paper, a more generalized dilated nested array (DNA) named multi-level dilated nested array (multi-level DNA), which further extends the original DNA to the general situation and improves the direction of arrival (DOA) estimation performance, is proposed. The original DNA, which consists of a nested array and a time-shifted array, possesses the capabilities of handling more sources and achieving improved estimation accuracy compared with the nested array. However, only one time-shifted array is employed in DNA and the performance improvement is quite limited. Here, a new multi-level DNA, which utilizes multiple time-shifted nested arrays, is proposed. The multi-level DNA can provide more degrees of freedom (DoFs), meanwhile its difference co-array is still hole-free. The closed form expression of uniform DoFs in multi-level DNA is derived. The corresponding DOA Cramer-Rao bound, which gives the low bound on the variance of estimated DOA, is deduced in detail and some properties related to it are concluded. In total, for the DOA estimation, multi-level DNA can detect more sources and achieve more accurate estimation performance compared with the original DNA. Numerical simulations are performed to verify the superiority of the proposed multi-level DNA.